The present invention relates generally to digital filter circuit arrangements and more particularly to a digital filter circuit arrangement capable of reducing a limit cycle generated when an input signal is not introduced into a digital filter.
A digital filter in which an analog signal is sampled, for example, with a specific sampling period T thereby to produce a sampled series signal, which is quantized, and a pulse code modulated (PCM) or difference modulated digital signal obtained by subjecting pulses to discontinuous level modulation is subjected to digital operation processing by a digital multiplier, a unit delay circuit which delays by a time equal to the above mentioned sampling period T, and an adder thereby to produce a digital signal as output has heretofore been known. An analog signal obtained by digital to analog (A/D) converting this output digital signal of the digital filter by means of a D/A converter becomes a signal which is the result of imparting a specific frequency characteristic to the original source analog signal of the input digital signal of the digital filter.
With a recursive digital filter which undergoes an operation as represented by the following difference equation as an example of such a digital filter, the generation of a limit cycle will be described. EQU y.sub.n =a.sub.0 x.sub.n -b.sub.1 y.sub.n-1 . . . ( 1)
In Eq. (1): y.sub.n is the value of the output signal of the digital filter at the time instant nT (where n is an integer, and T is the above mentioned sampling period); x.sub.n is the value of the input signal of the digital filter at the time instant nT; and a.sub.0 and b.sub.1 are respectively coefficients expressed by finite numbers of bits.
For the sake of simplicity of description, the above coefficients a.sub.0 and b.sub.1 and the output y.sub.n-1 will be considered to be continuous values (analog quantities), and the values of a.sub.0 =1.0, b.sub.1 =0.5, and y.sub.n-1 =1.0 will be taken. When there is no input digital signal of this digital filter, x.sub.n =0. Therefore, if this is substituted in Eq. (1), and calculation is carried out, the following values are obtained. ##STR1## When the values of the output signals of the digital filter are represented by continuous values in this manner, they can be represented substantially limitlessly by numerals below the decimal point.
However, the digital filter is a nonlinear system for digital operation of finite word length, and, moreover, "rounding off" is carried out in accompaniment with the operation. Here, the term "rounding off" means the addition of one (unity) to the succeeding lower bit of the required number of bits and corresponds to counting fractions of 0.5 and over as a whole number and disregarding the rest. For this reason, in the case where, for example, an infinite bit representation is processed by rounding off to 4 bits, the value of y.sub.n+5, y.sub.n+6, . . . in Eq. (2) becomes 0.0625 by rounding off, and the output of the digital filter in this case becomes as indicated in the following table when there is no input digital signal as mentioned above.
______________________________________ Analog 4-bit conversion Output analog Infinite bit representation value of actual conversion representa- by rounding output consider- value tion off ing rounding off ______________________________________ y.sub.n = -0.5 110000 . . . 1100 -0.5 y.sub.n+1 = 0.25 001000 . . . 0010 0.25 y.sub.n+2 = -0.125 111100 . . . 1111 -0.125 y.sub.n+3 = 0.0625 000010 . . . 0001 0.125 y.sub.n+4 = -0.0625 111110 . . . 1111 -0.125 y.sub.n+5 = 0.0625 000010 . . . 0001 0.125 . . . . . . . . . . . . ______________________________________ Note: In the above table, the bit representation is a complement representation of 2.
As is apparent from the above table, the digital output is repeated alternately as 0.125 and -0.125 as analog conversion values. This is the phenomenon called limit cycle.
When this limit cycle exists, a noise having a specific frequency spectrum is produced in the transmitted signal.
Accordingly, a method wherein masking is effected by impressing a random noise of white-noise character in order to render inconspicuous this noise having the specific frequency spectrum has heretofore been resorted to. This known method, however, has been accompanied by a problem in that it only makes the noise of the specific frequency spectrum inconspicuous, and noise is distributed over the entire frequency band.
In order to reduce a noise of a specific frequency spectrum of this nature, it is necessary to reduce the generation of a limit cycle.